F.3 WLS position solution

38.1713GPPNRRelease 17Requirements for Support of Assisted Global Navigation Satellite System (A-GNSS)TS

The WLS position solution problem is concerned with the task of solving for four unknowns; xu, yu, zu the receiver coordinates in a suitable frame of reference (usually ECEF) and bu the receiver clock bias. It typically requires the following steps:

Step 1: Formation of pseudo-ranges

The observation of code phase reported by the UE for each satellite SVi is related to the pseudo-range/c modulo the "gnss‑CodePhaseAmbiguity". For the formation of pseudo-ranges, the integer number of milliseconds to be added to each code-phase measurement has to be determined first. Since 1 ms corresponds to a travelled distance of 300 km, the number of integer ms can be found with the help of reference location and satellite ephemeris. The distance between the reference location and each satellite SVi is calculated and the integer number of milli-seconds to be added to the UE code phase measurements is obtained.

Step 2: Correction of pseudo-ranges for the GNSS-GNSS time offsets

In the case that the UE reports measurements for more than a single GNSS, the pseudo-ranges are corrected for the time offsets between the GNSSs relative to the selected reference time using the GNSS-GNSS time offsets available at the SS:

,

where is the measured pseudo-range of satellite i of GNSSm. The system time of GNSSk is the reference time frame, andis the available GNSS-GNSS time offset, and c is the speed of light.

Step 3: Formation of weighting matrix

The UE reported "codePhaseRMSError" values are used to calculate the weighting matrix for the WLS algorithm [7]. According to TS 36.355 [3], the encoding for this field is a 6 bit value that consists of a 3 bit mantissa, Xi and a 3 bit exponent, Yi for each SVi:

The weighting Matrix W is defined as a diagonal matrix containing the estimated variances calculated from the "codePhaseRMSError" values:

Step 4: WLS position solution

The WLS position solution is described in reference [7] and usually requires the following steps:

1) Computation of satellite locations at time of transmission using the ephemeris parameters and user algorithms defined in the relevant ICD of the particular GNSS. The satellite locations are transformed into WGS-84 reference frame, if needed.

2) Computation of clock correction parameters using the parameters and algorithms as defined in the relevant ICD of the particular GNSS.

3) Computation of atmospheric delay corrections using the parameters and algorithms defined in the relevant ICD of the particular GNSS for the ionospheric delay, and using the Gupta model in reference [8] p. 121 equation (2) for the tropospheric delay. For GNSSs which do not natively provide ionospheric correction models (e.g., GLONASS), the ionospheric delay is determined using the available ionospheric model adapted to the particular GNSS frequency.

4) The WLS position solution starts with an initial estimate of the user state (position and clock offset). The Reference Location is used as initial position estimate. The following steps are required:

a) Calculate geometric range (corrected for Earth rotation) between initial location estimate and each satellite included in the UE measurement report.

b) Predict pseudo-ranges for each measurement including clock and atmospheric biases as calculated in 1) to 3) above and defined in the relevant ICD of the particular GNSS and [7].

c) Calculate difference between predicted and measured pseudo-ranges

d) Calculate the "Geometry Matrix" G as defined in [7]:

with where rsGNSSm,i is the satellite position vector for SVi of GNSSm (calculated in 1) above), and is the estimate of the user location.

e) Calculate the WLS solution according to [7]:

f) Adding the to the initial state estimate gives an improved estimate of the state vector:

.

5) This new state vector can be used as new initial estimate and the procedure is repeated until the change in is sufficiently small.

Step 5: Transformation from Cartesian coordinate system to Geodetic coordinate system

The state vector calculated in Step 4 contains the UE position in ECEF Cartesian coordinates together with the UE receiver clock bias relative to the selected GNSS system time. Only the user position is of further interest. It is usually desirable to convert from ECEF coordinates xu, yu, zu to geodetic latitude ϕ , longitude  and altitude h on the WGS-84 reference ellipsoid.

Step 6: Calculation of "2-D Position Errors"

The latitude ϕ / longitude obtained after Step 5 is used to calculate the 2-D position error.

Annex G (informative):
Change history

Change history

Date

Meeting

TDoc

CR

Rev

Cat

Subject/Comment

New version

2018-11

RAN4#89

R4-1814423

TS baseline created from TS 36.171.

0.1.0

2018-11

RAN4#89

R4-1814424

Updates from e-mail discussion

0.2.0

2018-12

RAN#82

RP-182325

V1.0.0 is submitted to RAN for 1-step approval

1.0.0

2018-12

RAN#82

Approved by plenary – Rel-15 spec under change control

15.0.0

2019-03

RAN#83

RP-190402

0001

1

F

CR on A-GNSS in 38.171

15.1.0

2019-12

RAN#86

RP-193002

0008

1

F

CR to TS 38.171: Corrections to A-GNSS requirements with NR

15.2.0

2020-03

RAN#87

RP-200409

0009

1

F

Update of the Note 1 in the Power level and satellite allocation table for the Sensitivity Coarse time assistance requirements

15.3.0

2020-03

RAN#87

RP-200409

0010

F

Editorial change to TS 37.571-1 title

15.3.0

2020-06

RAN#88

RP-201055

0011

1

B

CR for TS38.171, Introduction of BDS B1C in A-GNSS

16.0.0

2021-06

RAN#92

RP-211077

0012

F

Addition of missing data for BDS B1C

16.1.0

2021-09

RAN#93

RP-211925

0015

F

Big CR to TS 38.171 on requirements maintenance (Rel-16)

16.2.0

2021-12

RAN#94

RP-212853

0016

F

Frequency bands for testing of A-GNSS sensitivity requirements

16.3.0

Change history

Date

Meeting

TDoc

CR

Rev

Cat

Subject/Comment

New version

2022-03

RAN#95

Update to Rel-17 version (MCC)

17.0.0

2022-06

RAN#96

RP-221653

0018

A

CR on TS 38.171 requirements for support of A-GNSS

17.1.0

2022-09

RAN#97

RP-222055

0019

B

Big CR for 38.171 (Rel-17)

17.2.0